Another important aspect of the existing Riemann-Roch theory is functoriality. We extend the method to the relative case i.e. morphisms between curves like in [1]} (except that we also cover its geometric counterpart). It is also compatible with functorial approach that gives Grothendieck-Riemann-Roch theorem for one-dimensional global fields (see for example [2]} for the number field case). Surprisingly this can be achieved by using a natural renormalisation of the Haar measure on the ring of adeles through global Poisson summation formulae.
